Chapter 16 DCF with Inflation and Taxation
LEARNING OBJECTIVES
1.
2.
3.
4.
5.
6.
Explain the impact of inflation on interest rates and define and distinguish between
real and nominal (money) interest rates.
Explain the difference between the real terms and nominal terms approaches to
investment appraisal.
Explain the impact of tax on DCF appraisals.
Calculate the tax cash flows associated with capital allowances and incorporate them
into NPV calculations.
Calculate the tax cash flows associated with taxable profits and incorporate them
into NPV calculations.
Explain the impact of working capital on an NPV calculation and incorporate
working capital flows into NPV calculations.
DCF with
Inflation
and
Taxation
Inflation
Specific
Inflation
General
Inflation
Interest
Rate
Real
Interest
Rate
Taxation
Money
Interest
Rate
Fisher's
Equation
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Capital
Allowances
Incorporating
Working
Capital
1.
Inflation
1.1
Specific and general inflation
1.1.1 It is important to adapt investment appraisal methods to cope with the phenomenon of
price movement. Future rates of inflation are unlikely to be precisely forecasted;
nevertheless, we will assume in the analysis that follows that we can anticipate inflation
with reasonable accuracy.
1.1.2 Two types of inflation can be distinguished.
(a)
(b)
Specific inflation refers to the price changes of an individual good or service.
General inflation is the reduced purchasing power of money and is
measured by an overall price index which follows the price changes of a
‘basket’ of goods and services through time. => affect discount rate
Even if there was no general inflation, specific items and sectors might experience price
rises.
1.1.3 Inflation creates two problems for project appraisal.
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1.2
(a)
The estimation of future cash flows is made more troublesome. The project
appraiser will have to estimate the degree to which future cash flows will be
inflated.
(b)
The rate of return required by the firm’s security holders, such as shareholders,
will rise if inflation rises. Thus, inflation has an impact on the discount rate
used in investment evaluation.
Real and money interest rate
1.2.1 The money (nominal or market) interest rate incorporates inflation. When the nominal
rate of interest is higher than the rate of inflation, there is a positive real rate. When the
rate of inflation is higher than the nominal rate of interest, the real rate of interest will
be negative.
1.2.2
Fisher’s (1930) Equation
The generalized relationship between real rates of interest and nominal rate of
interest is expressed as follow under Fisher’s equation:
(1 + i) = (1 + r) (1 + h)
Where h = inflation rate
r = real interest rate
i = nominal interest rate
1.2.3
Example 1
$1,000 is invested in an account that pays 10% interest pa. Inflation is currently 7%
pa. Find the real return on the investment.
(1 + 10%) = (1 + r) (1 + 7%)
Solution:
Real return = $1,000 × 1.1/1.07 = $1.028. A return of 2.8%.
Question 1
N16-3
If the real rate of interest is 8% and the rate of inflation is 5%, what should the money rate
of interest be?
Solution:
1.3
Money cash flows and real cash flows
1.3.1 We have now established two possible discount rates, the money discount rate and
the real discount rate. There are two alternative ways of adjusting for the effect of
future inflation on cash flows.
(a)
(b)
1.3.2
The first is to estimate the likely specific inflation rates for each of the inflows
and outflows of cash and calculate the actual monetary amount paid or received
in the year that the flow occurs. This is the money (nominal) cash flow.
The other possibility is to measure the cash flows in terms of real prices. That
is, all future cash flows are expected in terms of, say, Time 0’s prices. With real
cash flows, future cash flows are expressed in terms of constant purchasing
power.
Example 2
Storm Co is evaluating Project X, which requires an initial investment of $50,000.
Expected net cash flows are $20,000 pa for four years at today’s prices. However
these are expected to rise by 5.5% pa because of inflation. The firm’s cost of capital
is 15% => money cost of capital. Find the NPV by:
(a)
(b)
discounting money cash flows
discounting real cash flows.
Solution:
(a)
Discounting money cash flow at the money rate: The cash flows at today’s
prices are inflated by 5.5% for every year to take account of inflation and
convert them into money flows. They are then discounted using the money
cost of capital.
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Note: The question simply refers to the ‘firm’s cost of capital’. You can assume this
is the money rate – if you are given a real rate the examiner will always specify.
Time
Money cash flow ($)
0
1
2
(50,000)
21,100
= 20,000 x (1+5.5%)
22,261
3
4
= 20,000 x (1+5.5%)2
23,485
24,776
Discount rate
@15%
1.000
0.870
(50,000)
18,357
0.756
16,829
0.658
0.572
15,453
14,172
NPV =
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PV ($)
14,811
(b)
Calculate the real rate by removing the general inflation from the money cost of
capital:
(1 + r) = (1 + i) / (1 + h)
= (1 + 15%) / (1 + 5.5%)
= 1.09
r = 9%
The real rate can now be applied to the real flows without any further adjustments.
Time
Real cash flow
($)
Discount rate
@ 9%
PV ($)
0
1–4
(50,000)
20,000
1
3.240
(50,000)
64,800
NPV =
14,800
Note: Differences due to rounding.
2.
Taxation and Investment Appraisal
2.1
Taxation
2.1.1 Taxation can have an important impact on project viability. If management are
implementing decisions that are shareholder wealth enhancing, they will focus on the
cash flows generated which are available for shareholders. Therefore, they will
evaluate the after-tax cash flows of a project.
2.1.2 Payments of tax, or reductions of tax payments, are cash flows and ought to be
considered in DCF analysis. Assumptions which may be stated in questions are as
follows.
(a)
Tax is payable in the year following the one in which the taxable profits are
made. Thus, if a project increases taxable profits by $10,000 in year 2, there will
be a tax payment, assuming tax at 30%, of $3,000 in year 3.
(b)
Net cash flows from a project should be considered as the taxable profits (not
just the taxable revenues) arising from the project.
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2.2
Capital allowances (tax-allowable depreciation, or writing down allowances
(WDAs) or depreciation allowances)
2.2.1 Writing down allowance is used to reduce taxable profits, and the consequent
reduction in a tax payment should be treated as a cash saving from the acceptance of
a project.
2.2.2
Example 3
ABC Ltd is considering a project which will require the purchase of a machine for
$1,000,000 at time zero. This machine will have a scrap value at the end of its fouryear life: this will be equal to its written-down value. Inland Revenue Department
(IRD) permits a 25% declining balance writing-down allowance on the machine
each year. Corporation tax, at a rate of 30% of taxable income, is payable. ABC
Ltd’s required rate of return is 12%. Operating cash flows, excluding depreciation,
and before taxation, are forecast to be:
Time (year)
Cash flows before tax
1
$
2
$
3
$
4
$
400,000
400,000
220,000
240,000
Note: All cash flows occur at year ends.
In order to calculate the NPV, first calculate the annual WDA. Note that each year
the WDA is equal to 25% of the asset value at the start of the year.
Years
0
1
2
3
4
Annual WDA ($)
Written-down value ($)
0
1,000,000 x 25% = 250,000
750,000 x 25% = 187,500
562,500 x 25% = 140,625
421,875 x 25% = 105,469
1,000,000
750,000
562,500
421,875
316,406
The next step is to derive the project’s incremental taxable income and to calculate
the tax payments.
Time (year)
1
2
3
4
$
$
$
$
400,000
400,000
220,000
240,000
Net income before WDA
and tax
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Less: WDA
250,000
187,500
140,625
105,469
Taxable profit
150,000
212,500
79,375
134,531
Tax payable at 30%
45,000
63,750
23,813
40,359
Finally, the total cash flows and NPV are calculated.
Time (year)
0
1
2
3
4
$
$
$
$
$
(1,000,000)
400,000
400,000
220,000
240,000
Incremental cash flow
before tax
Sale of machine
Tax payable
Net cash flows
316,406
0
(45,000)
(63,750)
(23,813)
(40,359)
(1,000,000)
355,000
336,250
196,187
516,047
1
0.8929
0.7972
0.7118
0.6355
(1,000,000)
316,980
268,059
139,646
327,948
Discount factor @12%
Discounted cash flow
NPV = $52,633
The assumption that machine can be sold at the end of the fourth year, for an amount
equal to the written-down value, may be unrealistic. It may turn out that the machine
is sold for the larger sum of $440,000. If this is the case, a balancing charge will
need to be made, because by the end of the third year IRD have already permitted
write-offs against taxable profit such that the machine is shown as having a writtendown value of $421,875. A year later its market value is found to be $440,000. The
balancing charge is equal to the sale value at Time 4 minus the written-down value
at Time 3, viz:
$440,000 – $421,875 = $18,125
Taxable profits for year 4 are now:
$
240,000
18,125
Pre-tax cash flows
Plus balancing charge
258,125
This result in a tax payment of $258,125 x 0.3 = $77,438 rather than $40,359.
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Of course, the analyst does not have to wait until the actual sale of the asset to make
these modifications to a proposed project’s projected cash flows. It may be possible
to estimate a realistic scrap value at the outset.
An alternative scenario, where the scrap value is less than the Year 4 written-down
value, will require a balancing allowance. If the disposal value is $300,000 then
the machine cost the firm $700,000 ($1,000,000 – $300,000) but the tax writtendown allowances amount to only $683,594 ($1,000,000 – $316,406). The firm will
effectively be overcharged by IRD. In this case a balancing adjustment, amount to
$16,406 ($700,000 – $683,594), is made to reduce the tax payable.
$
240,000
Pre-tax cash flows
Less: Annual writing-down allowance
Less: Balancing allowance
3.
3.1
3.2
Taxable profits
118,125
Tax payable @ 30%
35,438
Incorporating Working Capital
(Jun 09, Dec 09)
Investment in a new project often requires an additional investment in working
capital, i.e. the difference between short-term assets and liabilities.
The treatment of working capital is as follows:
(a)
(b)
(c)
3.3
(105,469)
(16,406)
Initial investment is a cost at the start of the project.
If the investment is increased during the project, the increase is a relevant cash
outflow.
At the end of the project all the working capital is released and treated as
cash inflow.
Example 4
A company expects sales for a new project to be $225,000 in the first year growing
at 5% pa. The project is expected to last for 4 years. Working capital equal to 10%
of annual sales is required and needs to be in place at the start of each year. Calculate
the working capital flows for incorporation into the NPV calculation.
Solution:
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Calculate the absolute amounts of working capital needed over the project:
Year
0
1
2
3
4
$
$
$
$
$
225,000
236,250
248,063
260,466
23,625
24,806
26,047
Sales
Working capital (10% sales)
22,500
Work out the incremental investment required each year (remember that the full
investment is released at the end of the project):
Year
0
1
2
3
4
$
$
$
$
$
23,625 –
24,806 –
26,047 –
22,500
23,625
24,806
(1,125)
(1,181)
(1,241)
Working
Working capital investment
4.
(22,500)
26,047
General layout of cash flow preparation
(Dec 10, Jun 11, Jun 13)
4.1
The general layout can be shown as follows:
Year
0
1
2
3
4
$000
$000
$000
$000
$000
Sales
X
X
X
Costs
(X)
(X)
(X)
X
X
X
(X)
(X)
(X)
X
X
X
Operating cash flows
Taxation
Tax benefit of CAs
Capital expenditure and scrap value
(X)
Working capital changes
(X)
(X)
(X)
(X)
X
Net cash flows
(X)
X
X
X
X
Discount factor
X
X
X
X
X
(X)
X
X
X
X
Present value
4.2
X
As for the PBE examination, it applies the simplified version to calculate the operation
cash flow (OCF):
(Dec 13)
OCF = Earnings before interest and tax (EBIT) + Depreciation – Tax
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Examination Style Questions
Question 2
(a) The financial manager of FIN Company presents the following project:
Year
0
1
2
$
$
$
1,000,000
1,000,000
Operating costs
250,000
250,000
Overhead
90,000
90,000
Depreciation
600,000
600,000
Taxes (17%)
10,200
10,200
Cost of machinery
1,200,000
Revenue
Required:
(i)
(ii)
Determine the cash flows of the project in Year 0, Year 1, and Year 2 respectively.
(3 marks)
Discuss the possible impacts and re-determine all the cash flows of the project in (i)
if now the financial manager predicts that the project will also lead to an increase
in its net working capital by $100,000. (Explain net working capital first, then
discuss the possible impacts and then re-calculate all the cash flows.)
(4 marks)
(iii) Discuss the possible impacts and re-determine all the cash flows of the project in (i)
if now the financial manager expects that the machinery has a salvage value of
$200,000 at the end of Year 2.
(5 marks)
(iv) Discuss the possible impacts and re-determine all the cash flows of the project in (i)
if now the financial manager adds that $300,000 was spent last year on research and
development for this project.
(2 marks)
(b)
The financial manager further presents that the internal rate of return (IRR) method is
the best method in evaluating investment appraisals.
Required:
(i)
(ii)
Determine the IRR of the project using the results in (a)(i).
(2 marks)
Based on the IRR, should the company accept the project? Discuss one
disadvantage of using IRR. Make your own assumptions if necessary.
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(4 marks)
(Total 20 marks)
(HKIAAT PBE Paper III Financial Management December 2007 Q1)
Question 3 – NPV with real and nominal cash flows
Suppose the financial manager is considering a project with the following cash flows before
allowing for inflation:
Year
0
1
Cash flow ($)
– 800,000
400,000
2
3
400,000
400,000
Real discount rate of the project is 3%.
Expected annual inflation for the next three years is 4%.
Expected nominal market return is 10%.
Nominal risk-free return is 6%.
Required:
(a)
(b)
(c)
Determine the NPV of the project using real cash flows and discount rate.
(3 marks)
Determine the NPV of the project using the money (nominal) cash flows and discount
rate.
(4 marks)
Would you prefer to use real cash flows and discount rate or money (nominal) cash
flows and discount rate? Explain.
(3 marks)
(HKIAAT PBE Paper III Financial Management December 2007 Q4(a))
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Question 4 – NPV with tax allowance
Hendil plc plans to invest £1 million in a new product range and has forecast the following
financial information:
Year
1
2
3
4
70,000
90,000
100,000
75,000
Average selling price (£/unit)
40
45
51
51
Average variable costs (£/unit)
30
28
27
27
500,000
500,000
500,000
500,000
Sales volume (units)
Incremental cash fixed costs (£/year)
The above cost forecasts have been prepared on the basis of current prices and no account has
been taken of inflation of 4% per year on variable costs and 3% per year on fixed costs. Working
capital investment accounts for £200,000 of the proposed £1 million investment and machinery
for £800,000.
Hendil uses a four-year evaluation period for capital investment purposes, but expects the new
product range to continue to sell for several years after the end of this period. Capital
investments are expected to pay back within two years on an undiscounted basis, and within
three years on a discounted basis.
The company pays tax on profits in the year in which liabilities arise at an annual rate
of 30% and claims capital allowances on machinery on a 25% reducing balance basis.
Balancing allowances or charges are claimed only on the disposal of assets.
The ordinary shareholders of Hendil plc require an annual return of 12%. Its ordinary shares
are currently trading on the stock market at £1·80 per share. The dividend paid by the company
has increased at a constant rate of 5% per year in recent years and, in the absence of further
investment, the directors expect this dividend growth rate to continue for the foreseeable future.
Required:
(a)
(b)
(c)
Using Hendil plc’s current average cost of capital of 11%, calculate the net present value
of the proposed investment.
(15 marks)
Calculate, to the nearest month, the payback period and the discounted payback period of
the proposed investment.
(4 marks)
Discuss the acceptability of the proposed investment and explain ways in which your net
present value calculation could be improved.
(6 marks)
(Total 25 marks)
N16-13
(Amended ACCA Paper 2.4 Financial Management and Control December 2006 Q1)
Question 5 – NPV and IRR
Charm plc, a software company, has developed a new game, ‘Fingo’, which it plans to launch
in the near future. Sales of the new game are expected to be very strong, following a favourable
review by a popular PC magazine. Charm plc has been informed that the review will give the
game a ‘Best Buy’ recommendation. Sales volumes, production volumes and selling prices for
‘Fingo’ over its four-year life are expected to be as follows.
Year
Sales and production (units)
1
150,000
2
70,000
3
60,000
4
60,000
£25
£24
£23
£22
Selling price (£ per game)
Financial information on ‘Fingo’ for the first year of production is as follows:
Direct material cost
Other variable production cost
Fixed costs
£5.40 per game
£6.00 per game
£4.00 per game
Advertising costs to stimulate demand are expected to be £650,000 in the first year of
production and £100,000 in the second year of production. No advertising costs are expected
in the third and fourth years of production. Fixed costs represent incremental cash fixed
production overheads. ‘Fingo’ will be produced on a new production machine costing £800,000.
Although this production machine is expected to have a useful life of up to ten years,
government legislation allows Charm plc to claim the capital cost of the machine against the
manufacture of a single product. Capital allowances will therefore be claimed on a straight-line
basis over four years.
Charm plc pays tax on profit at a rate of 30% per year and tax liabilities are settled in the year
in which they arise. Charm plc uses an after-tax discount rate of 10% when appraising new
capital investments. Ignore inflation.
Required:
(a)
(b)
Calculate the net present value of the proposed investment and comment on your findings.
(11 marks)
Calculate the internal rate of return of the proposed investment and comment on your
findings.
(5 marks)
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(c)
Discuss the reasons why the net present value investment appraisal method is preferred
to other investment appraisal methods such as payback, return on capital employed and
internal rate of return.
(9 marks)
(Total 25 marks)
(ACCA Paper 2.4 Financial Management and Control June 2006 Q5)
Question 6 – NPV with inflation
Trecor Co plans to buy a new machine to meet expected demand for a new product, Product T.
This machine will cost $250,000 and last for four years, at the end of which time it will be sold
for $5,000. Trecor Co expects demand for Product T to be as follows:
Year
Demand (units)
1
35,000
2
40,000
3
50,000
4
25,000
The selling price for Product T is expected to be $12.00 per unit and the variable cost of
production is expected to be $7.80 per unit. Incremental annual fixed production overheads of
$25,000 per year will be incurred. Selling price and costs are all in current price terms.
Selling price and costs are expected to increase as follows:
Increase
Selling price of Product T:
3% per year
Variable cost of production:
Fixed production overheads:
4% per year
6% per year
Other information:
Trecor Co has a real cost of capital of 5.7% and pays tax at an annual rate of 30% one year in
arrears. It can claim capital allowances on a 25% reducing balance basis. General inflation is
expected to be 5% per year.
Trecor Co has a target return on capital employed of 20%. Depreciation is charged on a straightline basis over the life of an asset.
Required:
(a)
(b)
Calculate the net present value of buying the new machine and comment on your findings
(work to the nearest $1,000).
(13 marks)
Calculate the before-tax return on capital employed (accounting rate of return) based on
the average investment and comment on your findings.
(5 marks)
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(c)
Discuss the strengths and weaknesses of internal rate of return in appraising capital
investments.
(7 marks)
(ACCA F9 Financial Management Pilot Paper Q4)
Question 7 – NPA with tax allowance and IRR
Duo Co needs to increase production capacity to meet increasing demand for an existing
product, ‘Quago’, which is used in food processing. A new machine, with a useful life of four
years and a maximum output of 600,000 kg of Quago per year, could be bought for $800,000,
payable immediately. The scrap value of the machine after four years would be $30,000.
Forecast demand and production of Quago over the next four years is as follows:
Year
Demand (units)
1
1.4 million
2
1.5 million
3
1.6 million
4
1.7 million
Existing production capacity for Quago is limited to one million kilograms per year and the
new machine would only be used for demand additional to this.
The current selling price of Quago is $8.00 per kilogram and the variable cost of materials is
$5.00 per kilogram. Other variable costs of production are $1.90 per kilogram. Fixed costs of
production associated with the new machine would be $240,000 in the first year of production,
increasing by $20,000 per year in each subsequent year of operation.
Duo Co pays tax one year in arrears at an annual rate of 30% and can claim capital allowances
(tax-allowable depreciation) on a 25% reducing balance basis. A balancing allowance is
claimed in the final year of operation.
Duo Co uses its after-tax weighted average cost of capital when appraising investment projects.
It has a cost of equity of 11% and a before-tax cost of debt of 8·6%. The long-term finance of
the company, on a market-value basis, consists of 80% equity and 20% debt.
Required:
(a)
Calculate the net present value of buying the new machine and advise on the acceptability
of the proposed purchase (work to the nearest $1,000).
(13 marks)
(b) Calculate the internal rate of return of buying the new machine and advise on the
acceptability of the proposed purchase (work to the nearest $1,000).
(4 marks)
(c) Explain the difference between risk and uncertainty in the context of investment appraisal,
N16-16
and describe how sensitivity analysis and probability analysis can be used to incorporate
risk into the investment appraisal process.
(8 marks)
(Total 25 marks)
(ACCA F9 Financial Management December 2007 Q2)
Question 8 – NPV
SC Co is evaluating the purchase of a new machine to produce product P, which has a short
product life-cycle due to rapidly changing technology. The machine is expected to cost $1
million. Production and sales of product P are forecast to be as follows:
Year
Production and sales (units/year)
1
2
3
4
35,000
53,000
75,000
36,000
The selling price of product P (in current price terms) will be $20 per unit, while the variable
cost of the product (in current price terms) will be $12 per unit. Selling price inflation is
expected to be 4% per year and variable cost inflation is expected to be 5% per year. No
increase in existing fixed costs is expected since SC Co has spare capacity in both space and
labour terms.
Producing and selling product P will call for increased investment in working capital. Analysis
of historical levels of working capital within SC Co indicates that at the start of each year,
investment in working capital for product P will need to be 7% of sales revenue for that year.
SC Co pays tax of 30% per year in the year in which the taxable profit occurs. Liability to tax
is reduced by capital allowances on machinery (tax-allowable depreciation), which SC Co can
claim on a straight-line basis over the four-year life of the proposed investment. The new
machine is expected to have no scrap value at the end of the four-year period.
SC Co uses a nominal (money terms) after-tax cost of capital of 12% for investment appraisal
purposes.
Required:
(a)
Calculate the net present value of the proposed investment in product P.
(12 marks)
(b)
Calculate the internal rate of return of the proposed investment in product P.
(c)
(3 marks)
Advise on the acceptability of the proposed investment in product P and discuss the
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limitations of the evaluations you have carried out.
(d)
(5 marks)
Discuss how the net present value method of investment appraisal contributes towards
the objective of maximising the wealth of shareholders.
(5 marks)
(Total 25 marks)
(ACCA F9 Financial Management June 2008 Q4)
Question 9 – NPV with inflation and Discounted Payback
PV Co is evaluating an investment proposal to manufacture Product W33, which has performed
well in test marketing trials conducted recently by the company’s research and development
division. The following information relating to this investment proposal has now been prepared.
Initial investment
Selling price (current price terms)
Expected selling price inflation
$2 million
$20 per unit
3% per year
Variable operating costs (current price terms)
Fixed operating costs (current price terms)
Expected operating cost inflation
$8 per unit
$170,000 per year
4% per year
The research and development division has prepared the following demand forecast as a result
of its test marketing trials. The forecast reflects expected technological change and its effect on
the anticipated life-cycle of Product W33.
Year
Demand (units)
1
60,000
2
70,000
3
120,000
4
45,000
It is expected that all units of Product W33 produced will be sold, in line with the company’s
policy of keeping no inventory of finished goods. No terminal value or machinery scrap value
is expected at the end of four years, when production of Product W33 is planned to end. For
investment appraisal purposes, PV Co uses a nominal (money) discount rate of 10% per year
and a target return on capital employed of 30% per year. Ignore taxation.
Required:
(a)
(b)
Identify and explain the key stages in the capital investment decision-making process,
and the role of investment appraisal in this process.
(7 marks)
Calculate the following values for the investment proposal:
(i) net present value;
(ii) internal rate of return;
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(iii) return on capital employed (accounting rate of return) based on average investment;
and
(iv) discounted payback period.
(c)
(13 marks)
Discuss your findings in each section of (b) above and advise whether the investment
proposal is financially acceptable.
(5 marks)
(Total 25 marks)
(ACCA F9 Financial Management June 2009 Q2)
N16-19